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[SCREENSHOT INCLUDED] The position of a particle moving along a coordinate plane is s = sqrt(1+5t), with s in meters and t and seconds. What is the particle's velocity when t = 3 sec?

SCREENSHOT INCLUDED The position of a particle moving along a coordinate plane is s sqrt15t with s in meters and t and seconds What is the particles velocity wh class=

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Answer:

C) [tex]\frac{5}{8}[/tex] m/s

Step-by-step explanation:

[tex]s(t)=\sqrt{1+5t}[/tex]

[tex]v(t)=\frac{d[s(t)]}{dt}[/tex]

[tex]v(t)=\frac{d(\sqrt{1+5t})}{dt}[/tex]

[tex]v(t)=\frac{5}{2\sqrt{1+5t}}[/tex]

[tex]v(3)=\frac{5}{2\sqrt{1+5(3)}}[/tex]

[tex]v(3)=\frac{5}{2\sqrt{1+15}}[/tex]

[tex]v(3)=\frac{5}{2\sqrt{16}}[/tex]

[tex]v(3)=\frac{5}{2(4)}}[/tex]

[tex]v(3)=\frac{5}{8}[/tex]

Therefore, the particle's velocity after 3 seconds is [tex]\frac{5}{8}[/tex] m/s.

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